Image texture to partially mask part of material
TL;DR: Invert your mask image

"No idea what transparent black means, but it is not transparent."

It means that the area outside the image canvas will be considered transparent, as in Alpha value = 0, some image formats also have the ability to still save color for transparent areas, like PNG, and so will also paint that area black, besides making it transparent, in case you are not using the alpha map, or use it separately for other purposes.

In your particular image it is white all around the canvas borders, which generally means it opaque in terms of alpha channels, so it won't mix well with the remaining surrounding material.

Clipping in Blender will not work because as you already found out from the manual, the surrounding will be considered black which never matches your image border.

Don't use the Invert Cycles node in Blender, because it will invert the image color but also the black transparent area applied by the clipping effect, leading to surroundings that never match the current color of the image border.

You have to explicitly use an external application to invert the colors before using it in Blender.